1. Field of the Invention
The present invention relates to the field of transimpedance amplifiers.
2. Prior Art
A transimpedance amplifier converts an input current to an output voltage with a gain whose units are ohms. FIG. 1 shows a circuit that uses an operational amplifier (opamp) and two resistors to make a negative feedback amplifier with an inverting voltage gain. For this circuit, the equation for vo and the amplifier voltage gain vo/vi is:
vo=xe2x88x92vi*RF/R2xe2x80x83xe2x80x83(Equation 1)
vo/vi=xe2x88x92RF/R2xe2x80x83xe2x80x83(Equation 2)
The circuit node at the noninverting input terminal of the amplifier in FIG. 1 is a virtual ground. Because this node has zero impedance, the input network which consists of voltage source vi and resistor R2 can be replaced with a current source that has a magnitude of iin=vi/R2. FIG. 2. shows the modified amplifier circuit.
Equation 1 may be rewritten as:
vo=xe2x88x92RF*(vi/R2)=xe2x88x92RF*iinxe2x80x83xe2x80x83(Equation 3)
The ideal transimpedance amplifier gain can be written as:
vo/iin=xe2x88x92RFxe2x80x83xe2x80x83(Equation 4)
These equations have assumed that the amplifier has an infinite voltage gain. Since the ideal operational amplifier has no output voltage constraints, iin can be any magnitude (no overdrive condition). The magnitude of the gain of a real transimpedance amplifier is somewhat less than RF due to the finite gain of a real operational amplifier, and the input signal iin is limited in magnitude to the available output swing at vo divided by RF.
In classical feedback theory, the transfer function or closed-loop gain of a system with negative feedback is expressed as:
Transfer function=G/(1+GH)xe2x80x83xe2x80x83(Equation 5)
Where G is the gain in the forward path only and H is the gain in the feedback path only.
G and H are usually functions of frequency, that is, their magnitudes and their phase angles change with frequency. A common way of indicating this dependence is to write G and H as G(jxcfx89) and H(jxcfx89), where xcfx89 is radian frequency and j is {square root over (xe2x88x921)}.
The most important quantity in determining the stability of a negative feedback amplifier is the GH term in the denominator of Equation 5. The system""s loop gain (GH) is calculated with the feedback disconnected from the input summing node, but appropriately terminated. From Equation 5, if the loop gain GH equals xe2x88x921 (magnitude of 1 and phase of xe2x88x92180xc2x0), the transfer function is undefined because of division by zero and the system is unstable. Actually, if the absolute value of the loop gain GH is equal to or greater than 1 at the frequency where the phase of GH=xe2x88x92180xc2x0, then the amplifier is unstable.
This concept is the key to analyzing the stability of transimpedance amplifiers, and particularly to understanding why transimpedance amplifiers can become unstable when diode clamps are used to provide input overdrive capability.
The simplest practical transimpedance amplifier is shown in FIG. 3. Transistor Q1 and resistor RL functionally replace the opamp in FIG. 2 (the grounded emitter of the transistor may be considered the positive terminal of the opamp). The current in RF provides negative feedback from the amplifier""s output to its input. The forward gain (G in Equation 5) of the amplifier is:
G=xe2x88x92xcex2*RF||RLxe2x80x83xe2x80x83(Equation 6)
Where xcex2 is the transistor current gain
The feedback gain (H in equation 5) is xe2x88x921/RF, because the feedback is a current into the inverting amplifier input node. The loop gain is:
GH=xcex2*RF||RL/RF=xcex2*RL/(RL+RF)xe2x80x83xe2x80x83(Equation 7)
Equation 7 expresses only the DC or low frequency loop gain. xcex2, the transistor current gain, is really a function of frequency. Also there are capacitances in the circuit whose impedance is a function of frequency. The largest capacitance in this circuit that affects loop gain is Ccb, the capacitance of the transistor base-collector junction. This capacitance is in parallel with RF and RL. A greatly simplified expression for the loop gain as a function of frequency is (neglecting any frequency dependence of H):
G(jxcfx89)H=xcex2(jxcfx89)*RF||RL||(1/jxcfx89Ccb)/RF
                                                                                          G                  ⁡                                      (                    jω                    )                                                  ⁢                H                            =                                                β                  ⁡                                      (                    jω                    )                                                  *                RF                ⁢                                  "LeftDoubleBracketingBar"                  RL                  "RightDoubleBracketingBar"                                ⁢                                                      (                                                                  1                        /                        jω                                            ⁢                                              xe2x80x83                                            ⁢                                              C                        cb                                                              )                                    /                  RF                                                                                                        =                                                                    β                    ⁡                                          (                      jω                      )                                                        *                                      RL                                          RL                      +                      RF                                                                                        1                  +                                                            jω                      ⁢                                              xe2x80x83                                            ⁢                                              C                        cb                                            *                      RL                      *                      RF                                                              RL                      +                      RF                                                                                                                              (                  Equation          ⁢                      xe2x80x83                    ⁢          8                )            
With respect to amplifier stability, one way to gain some insight is to set the feedback resistor RF to zero, that is, set the amplifier to have minimum gain, maximum feedback, and maximum bandwidth. If it""s going to oscillate, it will oscillate under this condition. The result is:
G(jxcfx89)H=P(jxcfx89) with RF=0xe2x80x83xe2x80x83(Equation 9)
The capacitance Ccb doesn""t play a role, since it is shorted out. The only thing that matters is if xcex2(jxcfx89) is greater than one at a frequency where its phase is xe2x88x92180xc2x0. This is generally not the case, as otherwise, diode-connected transistors would oscillate.
The transimpedance amplifier in FIG. 4 differs from that of FIG. 3 in that Schottky diodes D1 and D2 have been added in parallel with feedback resistor RF. Without these clamping diodes, the magnitude of the input signal iin is limited to about (vccxe2x88x92VCEsat)/RF. With the clamping diodes, when iin is in positive overdrive, transistor Q1 turns on until the output voltage vo drops enough to forward bias Schottky diode D2, after which any additional input current iin passes through diode D2 and transistor Q1 to ground to maintain the output vo at one Schottky drop below the Vbe of transistor Q1. At the other extreme wherein iin is in negative overdrive, transistor Q1 will turn off until the load resistor RL pulls the output voltage vo high enough to forward bias Schottky diode D1, after which any additional negative input current iin passes through Schottky diode D1 to maintain the output vo at one Schottky diode drop above the Vbe of transistor Q1. Thus the diodes clamp the output voltage swing to 2*Vdiode peak to peak, even with large input signals or overdrive (note that the negative input current magnitude is ultimately limited by the resistor RL). When one of the diodes turns on, the effective feedback resistance drops from RF to Rdiode, which may be only a few ohms. Based on the analysis above (Equations 8 and 9), this reduction in gain and subsequent increase in bandwidth should not make the amplifier unstable.
FIG. 5 shows another common transimpedance amplifier topology that uses an emitter follower (transistor Q2) to buffer the load resistor RL from the feedback resistor RF. It has some advantages over the simple amplifier in FIG. 4. First, the open loop gain is larger: instead of G=xe2x88x92xcex2*RL||RF, it is:
xe2x80x83G=xe2x88x92xcex2*RLxe2x80x83xe2x80x83(Equation 10)
The larger open loop gain increases the overall transimpedance gain. Second, when the output is taken at the emitter of Q2 instead of at the collector of Q1, the amplifier has greater drive capability. The output voltages and output voltage swings are the same as for the transimpedance amplifier of FIG. 4. The loop gain GH of this amplifier is (H is still xe2x88x921/RF):
GH=xcex2RL/RFxe2x80x83xe2x80x83(Equation 11)
The loop gain of the amplifier without the emitter follower Q2 was shown to be:
GH=xcex2*RL/(RL+RF)xe2x80x83xe2x80x83(Equation 7)
With RF greater than  greater than RL, the difference in magnitude of the two equations is small. But when RF is very small, GH in Equation 11 becomes very big (the maximum loop gain increases by a factor of xcex2 due to transistor Q2). Additionally, the base-collector capacitance of transistor Q1 is no longer shorted out when RF is zero. This capacitance adds up to 90xc2x0 additional phase shift around the loop (there is a pole at 1/2xcfx80RL*Ccb). With a factor of xcex2 times more loop gain and the possibility of 90xc2x0 additional phase shift, this amplifier will oscillate when the transimpedance gain is small enough. Practically, the gain does become small enough when Schottky diode D1 or D2 turn on in overdrive, and the amplifier does become unstable.
Transimpedance amplifiers that provide moderate bandwidth and very large overdrive current capabilities while consuming a minimum amount of power supply current are disclosed. Existing transimpedance amplifier topologies use a quiescent current somewhat larger than the overdrive current that must be tolerated while the present invention reduces the value of the quiescent current and can tolerate bi-directional overdrive current several times larger than the current consumption of the circuit itself. The preferred embodiment of the invention is arranged such that stability of the circuit is ensured under all operating conditions, including overdrive conditions. Various embodiments are disclosed.